Donald Trump has vowed to crack down on illegal immigrants and cut taxes, but also insisted Americans have nothing to fear from his presidency.

In an interview with CBS's 60 Minutes, the President-elect made it clear he intends to aggressively pursue a conservative agenda.

On immigration, Mr Trump reaffirmed his campaign pledge to build a wall between the US and Mexico, although he conceded parts of it may be just a fence.

And he said as many as three million undocumented immigrants with criminal records would be deported or jailed.

"What we are going to do is get the people that are criminals and have criminal records, gang members, drug dealers," he said.

"We have a lot of these people, probably two million, it could be even three million, we are getting them out of our country or we are going to incarcerate."

He left the door open, however, on the fate of the millions of other hard-working immigrants in the country illegally.

"After the border is secured and after everything gets normalised, we're going to make a determination on the people that you're talking about who are terrific people," he said.

Immigration was one of three top legislative priorities, he said, the others being action to undo Barack Obama's signature healthcare reform but to keep some aspects of it, and a bill to cut taxes and simplify the tax code.

Mr Trump also pledged to name justices to the Supreme Court who are anti-abortion and pro-gun rights.

"The judges will be pro-life," he told CBS. "In terms of the whole gun situation," he added, "they're going to be very pro-Second Amendment."

Responding to the thousands of protesters who have massed in streets below Trump Tower headquarters, the billionaire said "I just don't think they know me".

He went on to tell those Americans who are scared of his presidency: "Don't be afraid. We are going to bring our country back."

He also confirmed he would forego the $400,000 salary that comes with the office of president.

"I'm not going to take the salary. I'm not taking it," he said. "I think I have to by law take $1, so I'll take $1 a year," he added.

Meanwhile, the President-elect has chosen the chairman of the Republican National Committee, Reince Priebus, to be his White House chief of staff.

In another development, former New York mayor Rudy Giuliani has suggested Mr Trump put his businesses in a blind trust.

"He should basically take himself out of it, and just be a passive participant in the sense that he has no decision-making, no involvement," Mr Giuliani said, adding that it would be "for the good of the country".